The demand for rare earth elements (REEs) is growing, while the future supply is uncertain. Their unique electronic characteristics make them irreplaceable, and the commercial value of pure fractions is high. A model-based simulation study is presented that compares batch chromatography with the twin-column MCSGP (multicolumn countercurrent solvent gradient purification) process for ion-exchange chromatography of the four-component system neodymium, samarium, europium, and gadolinium. The last three components are considered products with individual purity requirements of 99%. The twin-column process has been shown to be a good alternative to the batch process regarding modifier consumption and productivity since it enables internal recycling to achieve high purities. A new cut strategy for MCSGP is applied where subfractions are taken from each outlet. Two multiobjective optimizations with yield, solvent productivity, and productivity objectives show that the MCSGP process is a better alternative than batch chromatography.